Particle Tracking. For Bulk Material Handling Systems Using DEM Models. By: Jordan Pease

Transcription

1 Particle Tracking For Bulk Material Handling Systems Using DEM Models By: Jordan Pease

2 Introduction Motivation for project Particle Tracking Application to DEM models Experimental Results Future Work References and Acknowledgments

3 Motivation Bulk Handling Head Station

4 What is DEM? Motivation

5 Bulk Handling Particle Tracking Why Track Particles? Material Flow Chute Plugging Material Distribution Reduce Wear On: Chute Walls Liners Belt

6 Motion Estimation Techniques Feature-based methods Extract visual features (corners, textured areas) and track them over multiple frames Sparse motion fields, but more robust tracking Suitable when image motion is large (10s of pixels) Direct methods Directly recover image motion at each pixel from spatiotemporal image brightness variations Dense motion fields, but sensitive to appearance variations Suitable for video and when image motion is small

7 Particle Tracking Methods/Background Brownian Motion Particle Filter Optical Flow Phase Correlation Block-based Methods Differential Methods Horn-Schunck Black-Jepsen Buxton-Buxton Lucas-Kanade

8 Optical flow Definition: optical flow is the apparent motion of brightness patterns in the image Ideally, optical flow would be the same as the motion field Have to be careful: apparent motion can be caused by lighting changes without any actual motion

9 Optical Flow How to estimate pixel motion from image H to image I? Find pixel correspondences Key assumptions Color (Brightness) constancy: a point in H looks like a point in image I Small Motion: Objects move slowly (or access to high frame rate)

10 Optical Flow: Lucas-Kanade Method Assumes that the displacement of the image contents between two nearby instants (frames) is small and approximately constant.

11 Gray-scale image Example How to get more equations for a pixel? Spatial coherence constraint: pretend the pixel s neighbors have the same (u,v) If we use a 5x5 window, that gives us 25 equations per pixel

12 Uh oh!: We Have More Equations Than Unknowns Solution: solve least squares problem minimum least squares solution given by solution (in d) of: The summations are over all pixels in the K x K window This technique is Lucas Kanade Method!

13 Conditions for Solvability When is this solvable? A T A should be invertible Images must match! (size, pixel density etc.) A T A should not be too small eigenvalues λ 1 and λ 2 of A T A should not be too small A T A should be well-conditioned λ 1 / λ 2 should not be too large (λ 1 = larger eigenvalue)

14 Optical Flow Issues

15 Iterative Refinement Estimate velocity at each pixel using one iteration of Lucas and Kanade estimation Warp one image toward the other using the estimated flow field Refine estimate by repeating the process CSE 576, Spring Motion estimation

16 Optical Flow: Iterative Estimation estimate update Initial guess: Estimate: x 0 x (using d for displacement here instead of u) CSE 576, Spring Motion estimation

17 Optical Flow: Iterative Estimation estimate update Initial guess: Estimate: x 0 x CSE 576, Spring Motion estimation

18 Optical Flow: Iterative Estimation estimate update Initial guess: Estimate: x 0 x CSE 576, Spring Motion estimation

19 Optical Flow: Iterative Estimation x 0 x CSE 576, Spring Motion estimation

20 Optical Flow With Matlab Calibration Images

21 Results Input Image Warp Image Estimated Flow Field

22 Results Input Image Warp Image Estimated Flow Field

23 Results: Failed Run

24 Future Work Real-time Video

25 Results Input Images Warp Image Estimated Flow Field

26 References & Acknowledgements TAKRAF TENOVA Bulk Flow Analyst Overland Conveyor MIT CSAIL Group Richard Szeliski Steve Seitz Complete list of sources can be found on subsequent slides

27 Other Runs

28 Other Runs

29 Other Runs

30 Bibliography J. R. Bergen, P. Anandan, K. J. Hanna, and R. Hingorani. Hierarchical modelbased motion estimation. In ECCV 92, pp , Italy, May M. J. Black and P. Anandan. The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields. Comp. Vis. Image Understanding, 63(1):75 104, Shi, J. and Tomasi, C. (1994). Good features to track. In CVPR 94, pages , IEEE Computer Society, Seattle. Baker, S. and Matthews, I. (2004). Lucas-kanade 20 years on: A unifying framework: Part 1: The quantity approximated, the warp update rule, and the gradient descent approximation. IJCV, 56(3), CSE 576, Spring Motion estimation

31 Bibliography T. Darrell and A. Pentland. Cooperative robust estimation using layers of support. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(5): , May S. X. Ju, M. J. Black, and A. D. Jepson. Skin and bones: Multi-layer, locally affine, optical flow and regularization with transparency. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'96), pages , San Francisco, California, June M. Irani, B. Rousso, and S. Peleg. Computing occluding and transparent motions. International Journal of Computer Vision, 12(1):5--16, January H. S. Sawhney and S. Ayer. Compact representation of videos through dominant multiple motion estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(8): , August M.-C. Lee et al. A layered video object coding system using sprite and affine motion model. IEEE Transactions on Circuits and Systems for Video Technology, 7(1): , February CSE 576, Spring Motion estimation

32 Bibliography S. Baker, R. Szeliski, and P. Anandan. A layered approach to stereo reconstruction. In IEEE CVPR'98, pages , Santa Barbara, June R. Szeliski, S. Avidan, and P. Anandan. Layer extraction from multiple images containing reflections and transparency. In IEEE CVPR'2000, volume 1, pages , Hilton Head Island, June J. Shade, S. Gortler, L.-W. He, and R. Szeliski. Layered depth images. In Computer Graphics (SIGGRAPH'98) Proceedings, pages , Orlando, July ACM SIGGRAPH. S. Laveau and O. D. Faugeras. 3-d scene representation as a collection of images. In Twelfth International Conference on Pattern Recognition (ICPR'94), volume A, pages , Jerusalem, Israel, October IEEE Computer Society Press. P. H. S. Torr, R. Szeliski, and P. Anandan. An integrated Bayesian approach to layer extraction from image sequences. In Seventh ICCV'98, pages , Kerkyra, Greece, September CSE 576, Spring Motion estimation